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In this paper, the effects of disorder on the dynamical quantum phasetransitions (DQPTs) in the transverse-field anisotropic XY chain are studied bynumerically calculating the Loschmidt echo after quench. We obtain the formulafor calculating the Loschmidt echo of the inhomogeneous system in real space.By comparing the results with that of the homogeneous chain, we find that whenthe quench crosses the Ising transition, the small disorder will cause a newcritical point. As the disorder increases, more critical points of the DQPTswill occur, constituting a critical region. In the quench across theanisotropic transition, the disorder will cause a critical region near thecritical point, and the width of the critical region increases by thedisordered strength. In the case of quench passing through two critical lines,the small disorder leads to the system to have three additional criticalpoints. When the quench is in the ferromagnetic phase, the large disordercauses the two critical points of the homogeneous case to become a criticalregion. And for the quench in the paramagnetic phase, the DQPTs will disappearfor large disorder.

Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain